DTRT06(3)

✨ NAME ✨

Hey bestie! This is the dtrt06.f(3) page from the Library Functions Manual 💅. The name/source path shown is literally /home/abui...IN/dtrt06.f(3) — and yes, that's the whole NAME entry, we love a minimal queen. 👑

🛠️ SYNOPSIS 🛠️

🧩 Functions/Subroutines 🧩

subroutine DTRT06 (rcond, rcondc, uplo, diag, n, a, lda, work, rat)
    DTRT06

📚 Function/Subroutine Documentation 📚

subroutine DTRT06 (double precision rcond, double precision rcondc,
    character uplo, character diag, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( * ) work, double
    precision rat)
    DTRT06

🎯 Purpose 🎯

Okay so here's the tea, bestie: DTRT06 computes a test ratio comparing RCOND — the reciprocal condition number of a triangular matrix A — with RCONDC, which is the estimate computed by DTRCON. 🫶 If one estimate is zero and the other is non-zero, it uses info about the triangular matrix A to decide whether that underflow in the estimate is justified. No cap. ✨

🧾 Parameters 🧾

💖 RCOND 💖

RCOND is DOUBLE PRECISION. It's the estimate of the reciprocal condition number you get by forming the explicit inverse of matrix A and computing RCOND = 1/( norm(A) * norm(inv(A)) ). 💅

💖 RCONDC 💖

RCONDC is DOUBLE PRECISION. It's the estimate of the reciprocal condition number computed by DTRCON. 🎀

💖 UPLO 💖

UPLO is CHARACTER. It specifies whether matrix A is upper or lower triangular:

• = 'U': Upper triangular
• = 'L': Lower triangular

💖 DIAG 💖

DIAG is CHARACTER. It specifies whether or not matrix A is unit triangular:

• = 'N': Non-unit triangular
• = 'U': Unit triangular

💖 N 💖

N is INTEGER. It's the order of matrix A. Constraint: N >= 0. ✅

💖 A 💖

A is a DOUBLE PRECISION array, dimension (LDA,N). It's the triangular matrix A. Here's the breakdown:

• If UPLO = 'U', the leading n by n upper triangular part of array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced.
• If UPLO = 'L', the leading n by n lower triangular part of array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
• If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.

💖 LDA 💖

LDA is INTEGER. It's the leading dimension of array A. Constraint: LDA >= max(1,N). 🔥

💖 WORK 💖

WORK is a DOUBLE PRECISION array, dimension (N). 🧚

💖 RAT 💖

RAT is DOUBLE PRECISION. It's the test ratio. If both RCOND and RCONDC are nonzero, the formula is:

RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.

If RAT = 0, the two estimates are exactly the same. 💀

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

📍 Definition at line 119 of file dtrt06.f. 📍

DTRT06 is defined at line 119 of file dtrt06.f. 📌

👑 Author (generated page) 👑

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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And that's the whole page, bestie — cute sign-off time: the footer has LAPACK Version 3.12.0 and the path /home/abui...IN/dtrt06.f(3); there's no extra date line on this one. Bye! 💅✨